Question

which polynomial represents the area of the rectangle? 4x - 6 x + 1 4x^2 + 2x - 6 4x^2 - 2x - 6 4x^2 - 10x - 6 4x^2 - 6

Explanation:

Step1: Recall area formula

The area $A$ of a rectangle is given by $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=4x - 6$ and $w=x + 1$.

Step2: Expand the product

$(4x-6)(x + 1)=4x\times x+4x\times1-6\times x - 6\times1$.

Step3: Simplify the terms

$4x\times x=4x^{2}$, $4x\times1 = 4x$, $-6\times x=-6x$, and $-6\times1=-6$. Then $4x^{2}+4x-6x - 6=4x^{2}-2x - 6$.

Answer:

$4x^{2}-2x - 6$